Question

Write an equation to the exponential function. I’m in need of some help with this question.

Answer 1

First, notice that the given graph is the reflected over the x-axis and y-axis version of an exponential function of the form:

`y=ab^x.`

Now, the y-intercept of the graph is -3, therefore, the parent function has

`a=3.`

Now, the graph passes through the point (-1,-6), therefore, the parent function passes through (1,6). Solving

`6=3(b)^1,`

for b, we get:

`\begin{gathered} b=(6)/(3), \\ b=2. \end{gathered}`

Finally, we reflect the parent function over the x-axis and over the y-axis and get:

`y=-3(2)^(-x).`

Answer:

`y=-3(2)^(-x).`